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SashulF [63]
3 years ago
5

Simplify the following expression (3x^2y)^3

Mathematics
1 answer:
kolezko [41]3 years ago
6 0

Answer:

\large\boxed{\left(3x^2y\right)^3=27x^6y^3}

Step-by-step explanation:

\text{Use}\ (ab)^n=a^nb^n\ \text{and}\ (a^n)^m=a^{nm}\\\\\left(3x^2y\right)^3=3^3(x^2)^3y^3=27x^6y^3

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A Formula one car travels at 850 feet every 10 seconds. If the Car is 2550 feet from the finish line, How much time will it take
Vinvika [58]

Answer:

30 seconds

Step-by-step explanation:

speed= 850 feet / 10 seconds = 85 feet/ second

distance = 2550

time= distance/speed

= 2550 divided by 85

= 30 seconds

4 0
3 years ago
ABC is an isosceles triangle in which AC =BC.
aev [14]

Given:

ABC is an isosceles triangle in which AC =BC.

D and E are points on BC and AC such that CE=CD.

To prove:

Triangle ACD and BCE are congruent​.

Solution:

In triangle ACD and BCE,

AC=BC                  (Given)

AC\cong BC

\angle C\cong m\angle C                  (Common angle)

CD=CE                  (Given)

CD\cong CE

In triangles ACD and BCE two corresponding sides and one included angle are congruent. So, the triangles are congruent by SAS congruence postulate.

\Delta ACD\cong \Delta BCE           (SAS congruence postulate)

Hence proved.

3 0
3 years ago
Read 2 more answers
The sum of the first two terms of an infinite GP is 6 and each term is 5 times the sum of the succeeding termsthen the second te
kozerog [31]

Answer:

\dfrac{6}{7}.

Step-by-step explanation:

It is given that the sum of first two terms of an infinite GP is 6.

nth term of a GP is

a_n=ar^{n-1}

a+ar=6     ...(1)

Each term is 5 times the sum of the succeeding terms.

a_n=5(a_{n+1}+a_{n+2}+...+\infty)

ar^{n-1}=5(ar^n+ar^{n+1}+...+\infty)

ar^{n-1}=5ar^n(1+r+r^2+...+\infty)

Divide both sides by a.

r^{n-1}=5r^n(\dfrac{1}{1-r})    [\text{Sum of infinite GP}=\dfrac{a}{1-r}]

\dfrac{r^n}{r}=\dfrac{5r^n}{1-r}

\dfrac{1}{r}=\dfrac{5}{1-r}

1-r=5r

1=6r

\dfrac{1}{6}=r

The common ratio is 1/6.

Put r=1/6 in (1).

a+a(\dfrac{1}{6})=6

6a+a=36

7a=36

a=\dfrac{36}{7}

Second term ar=\dfrac{36}{7}\times \dfrac{1}{6}=\dfrac{6}{7}

Therefore, the second term is \dfrac{6}{7}.

4 0
2 years ago
Put the following equation of a line into slope-intercept form, simplifying all
ELEN [110]

Answer:

2/3x+8=y

Step-by-step explanation:

8x-12y=-96

8x+96=12y

8/12x+8=y

2/3x+8=y

5 0
3 years ago
Solve for x. 4x-5=9+20
pickupchik [31]

Answer:

x = 8.5

Step-by-step explanation:

4x-5=9+20   (evaluate right side)

4x - 5 = 29   (add 5 to both sides)

4x = 29 + 5

4x = 34   (divide both sides by 4)

x = 34/4

x = 8.5

7 0
3 years ago
Read 2 more answers
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